相关论文: Strichartz estimates for geophysical fluid equatio…

We identify a one-parameter family of inequalities for the Fourier transform whose limiting case is the restriction conjecture for the sphere. Using Stein's method of complex interpolation we prove the conjectured inequalities when the…

Many fundamental problems in fluid dynamics are related to the effects of solid boundaries. In general, they install sharp gradients and contribute to the developement of small-scale structures, which are computationally expensive to…

We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…

We establish a general slice theorem for the action of a locally convex Lie group on a locally convex manifold, which generalizes the classical slice theorem of Palais to infinite dimensions. We discuss two important settings under which…

We show how a complete mathematical description of a complicated physical phenomenon can be learned from observational data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality,…

This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…

We propose a theoretical method to decompose the solution of a Stokes flow past a body immersed in a confined fluid in two simpler problems, related separately to the two geometrical elements of these systems: (i) the body immersed in the…

A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to…

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the…

Most of the turbulent flows appearing in nature (e.g. geophysical and astrophysical flows) are subjected to strong rotation and stratification. These effects break the symmetries of classical, homogenous isotropic turbulence. In doing so,…

In this work, we study and extend a class of semi-Lagrangian exponential methods, which combine exponential time integration techniques, suitable for integrating stiff linear terms, with a semi-Lagrangian treatment of nonlinear advection…

We develop refined Strichartz estimates at $L^2$ regularity for a class of time-dependent Schr\"{o}dinger operators. Such refinements begin to characterize the near-optimizers of the Strichartz estimate, and play a pivotal part in the…

Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum and energy.…

We prove a Fourier restriction result, uniform over a certain collection of reference measures, for some indices in the Stein-Tomas range.

Uniqueness in the Calder\'on problem in dimension bigger than two was usually studied under the assumption that conductivity has bounded gradient. For conductivities with unbounded gradients uniqueness results have not been known until…

A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $L^p-L^q$ restriction…

We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…

We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…

In this article, we prove the analogue theorems of Stein-Tomas and Srtichartz on the discrete surface restrictions of Fourier-Hermite transforms associated with the normalized Hermite polynomials and obtain the Strichartz estimate for the…

This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of this work compared to previous studies is the absence of…